Saltwater QuenchOil Quench145152150150153147148155141140152146146158154152139151148143(a) Test the hypothesis that the mean hardness for the saltwater quenching process equals the mean hardness for the oil quenching process. Please use α=0.05 and assume equal variances.(b) Assuming that the variances and are equal, construct a 95% confidence interval on the difference in mean hardness.(c) Construct a 95% confidence interval on the ratio. Does the assumption made earlier of equal variances seem reasonable?Solution:Saltwater quench:

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Oil quench: (a) AssumeDo not reject H0, and conclude that there is no difference between the quenching processes.(b) (c) Since the interval of the ratio does include 1, the equal variance assumption is reasonable.Problem 5Solution:(a)(b)

(c) Problem 6:

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Solution:This is a hypergeometric distribution with N= 25 and n= 5, without replacement.(a) Given D= 2 and x= 0:(b) For the binomial approximation to the hypergeometric, and n = 5.This approximation, though close to the exact x= 0, violates the rule-of-thumb that be less than the suggested 0.1. The binomial approximation is not satisfactory in this case.(c) For, so the binomial approximation would be a satisfactory approximation the hypergeometric in this case.

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